# Percents from fraction models

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## Video transcript

- [Instructor] So we're told the square below represents one whole, so this entire square is a whole. And then they ask us what percent is represented by the shaded area, so why don't you pause this video and see if you can figure that out. So let's see. The whole is divided into one, two, three, four, five, six, seven, eight, nine, 10 equal sections, of which one, two, three, four, five, six, seven are actually filled in. That's the shaded area, so one way to think about it is 7/10 are shaded in, but how do we express this fraction as a percent? They're asking for a percent. Well remember, percent, it literally means per hundred. Cent, same root as the word 100. You see it cents or century, and so can we write this as per 100 instead of per 10? Well, seven per 10 is the same thing as 70 per 100, or 70%. And how did I go from 7/10 to 70 over 100? Well, I just multiply both the numerator and the denominator by 10. And once you do more and more percents, you'll get a hang of it. You'll say, "Oh, 7/10. "That's the same thing as 70 per 100, which is 70%." Let's do another example. Here, we're told 100% is shown on the following tape diagram, so just this amount right over here is 100%, and then they ask us what percent is represented by the entire tape diagram, so by this entire thing right over here. Pause this video and see if you can answer that. Well, one way to think about 100%, 100% is equivalent to a whole, and now we have three times as much as that for the entire tape diagram, so you could view this as three wholes, or you could say that's 100%. We have another 100% right over here. And then we have another 100% right over here, so the whole tape diagram, that would be 300%. Let's do another example. This is strangely fun. (laughs) Okay, and I'll see. It says the large rectangle below represents one whole. All right, so that's this whole thing is one whole. What percentage is represented by the shaded area? So pause the video and see if you can figure that out again. So let's just express it as a fraction first, so we have a total of one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 squares. So out of those 20 squares, we see that six of them are actually shaded in. So 6/20, could we write that as per 100? Well, let's see. To go from 20 to 100, I multiply by five, and so if I multiply the numerator by five, I'll get the same value. Six times five is 30, so six per 20 is the same thing as 30 per 100, which is the same thing as 30%, which literally means per 100, so this is 30%. Let's do one last example. Here we are told each large rectangle below represents one whole, so this is a whole, and then this whole thing right over here is another whole. What percentage is represented by the shaded area? Again, pause the video. See if you can answer that. So this one, we've shaded in a whole, so that is 100%, and then over here, we have shaded in one, two, three, 4/5 of the whole. So 4/5, if I wanted to express it as per 100, what would it be? Well, five time 20 is 100, so four times 20 is 80, so 4/5, or 80/100, is filled out here. We could say 80 per 100, which is the same thing as 80%, so this right over here is 80%. So what percent is represented by the shaded area? Well, we have 100%, and then we have 80%, so we have 180%. It's more than a whole. If you have a percentage that is larger than 100%, you're talking about something that is more than a whole, and then we see that. We have a whole right over here, and then we have 80% more than that.